1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 157,722 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  2 111       2020-03-18 fema… 0-18  e380000… nhs_bed…    27 mk454hr  East of E…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_bla…     9 bb12fd   North West
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_bro…    11 br33ql   London    
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_can…     9 ws111jp  Midlands  
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_cit…    12 n15lz    London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_enf…     7 en40dy   London    
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_ham…     6 dl62uu   North Eas…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_har…    24 ts232la  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_kin…     6 kt11eu   London    
## # … with 157,712 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##     date_report               nhs_region deaths
## 1    2020-03-01          East of England      0
## 2    2020-03-02          East of England      1
## 3    2020-03-03          East of England      0
## 4    2020-03-04          East of England      0
## 5    2020-03-05          East of England      0
## 6    2020-03-06          East of England      1
## 7    2020-03-07          East of England      0
## 8    2020-03-08          East of England      0
## 9    2020-03-09          East of England      1
## 10   2020-03-10          East of England      0
## 11   2020-03-11          East of England      0
## 12   2020-03-12          East of England      0
## 13   2020-03-13          East of England      1
## 14   2020-03-14          East of England      2
## 15   2020-03-15          East of England      2
## 16   2020-03-16          East of England      1
## 17   2020-03-17          East of England      1
## 18   2020-03-18          East of England      5
## 19   2020-03-19          East of England      4
## 20   2020-03-20          East of England      2
## 21   2020-03-21          East of England     11
## 22   2020-03-22          East of England     12
## 23   2020-03-23          East of England     11
## 24   2020-03-24          East of England     19
## 25   2020-03-25          East of England     26
## 26   2020-03-26          East of England     36
## 27   2020-03-27          East of England     38
## 28   2020-03-28          East of England     28
## 29   2020-03-29          East of England     43
## 30   2020-03-30          East of England     45
## 31   2020-03-31          East of England     70
## 32   2020-04-01          East of England     62
## 33   2020-04-02          East of England     64
## 34   2020-04-03          East of England     80
## 35   2020-04-04          East of England     71
## 36   2020-04-05          East of England     76
## 37   2020-04-06          East of England     71
## 38   2020-04-07          East of England     93
## 39   2020-04-08          East of England    111
## 40   2020-04-09          East of England     87
## 41   2020-04-10          East of England     74
## 42   2020-04-11          East of England     92
## 43   2020-04-12          East of England    101
## 44   2020-04-13          East of England     78
## 45   2020-04-14          East of England     61
## 46   2020-04-15          East of England     82
## 47   2020-04-16          East of England     74
## 48   2020-04-17          East of England     86
## 49   2020-04-18          East of England     64
## 50   2020-04-19          East of England     67
## 51   2020-04-20          East of England     67
## 52   2020-04-21          East of England     75
## 53   2020-04-22          East of England     67
## 54   2020-04-23          East of England     49
## 55   2020-04-24          East of England     66
## 56   2020-04-25          East of England     54
## 57   2020-04-26          East of England     48
## 58   2020-04-27          East of England     46
## 59   2020-04-28          East of England     58
## 60   2020-04-29          East of England     32
## 61   2020-04-30          East of England     45
## 62   2020-05-01          East of England     49
## 63   2020-05-02          East of England     29
## 64   2020-05-03          East of England     41
## 65   2020-05-04          East of England     19
## 66   2020-05-05          East of England     36
## 67   2020-05-06          East of England     31
## 68   2020-05-07          East of England     33
## 69   2020-05-08          East of England     33
## 70   2020-05-09          East of England     29
## 71   2020-05-10          East of England     22
## 72   2020-05-11          East of England     18
## 73   2020-05-12          East of England     21
## 74   2020-05-13          East of England     27
## 75   2020-05-14          East of England     26
## 76   2020-05-15          East of England     19
## 77   2020-05-16          East of England     26
## 78   2020-05-17          East of England     17
## 79   2020-05-18          East of England     25
## 80   2020-05-19          East of England     15
## 81   2020-05-20          East of England     26
## 82   2020-05-21          East of England     21
## 83   2020-05-22          East of England     13
## 84   2020-05-23          East of England     12
## 85   2020-05-24          East of England     17
## 86   2020-05-25          East of England     25
## 87   2020-05-26          East of England     14
## 88   2020-05-27          East of England     12
## 89   2020-05-28          East of England     17
## 90   2020-05-29          East of England     16
## 91   2020-05-30          East of England      9
## 92   2020-05-31          East of England      8
## 93   2020-06-01          East of England     17
## 94   2020-06-02          East of England     14
## 95   2020-06-03          East of England     10
## 96   2020-06-04          East of England      7
## 97   2020-06-05          East of England     12
## 98   2020-06-06          East of England      5
## 99   2020-06-07          East of England      9
## 100  2020-06-08          East of England      5
## 101  2020-06-09          East of England      6
## 102  2020-06-10          East of England      8
## 103  2020-06-11          East of England      0
## 104  2020-06-12          East of England      9
## 105  2020-06-13          East of England      5
## 106  2020-06-14          East of England      4
## 107  2020-06-15          East of England      7
## 108  2020-06-16          East of England      3
## 109  2020-06-17          East of England      7
## 110  2020-06-18          East of England      4
## 111  2020-06-19          East of England      7
## 112  2020-06-20          East of England      2
## 113  2020-06-21          East of England      3
## 114  2020-06-22          East of England      5
## 115  2020-06-23          East of England      4
## 116  2020-06-24          East of England      1
## 117  2020-03-01                   London      0
## 118  2020-03-02                   London      0
## 119  2020-03-03                   London      0
## 120  2020-03-04                   London      0
## 121  2020-03-05                   London      0
## 122  2020-03-06                   London      1
## 123  2020-03-07                   London      0
## 124  2020-03-08                   London      0
## 125  2020-03-09                   London      1
## 126  2020-03-10                   London      0
## 127  2020-03-11                   London      6
## 128  2020-03-12                   London      6
## 129  2020-03-13                   London     10
## 130  2020-03-14                   London     14
## 131  2020-03-15                   London     10
## 132  2020-03-16                   London     15
## 133  2020-03-17                   London     23
## 134  2020-03-18                   London     27
## 135  2020-03-19                   London     25
## 136  2020-03-20                   London     44
## 137  2020-03-21                   London     49
## 138  2020-03-22                   London     54
## 139  2020-03-23                   London     63
## 140  2020-03-24                   London     87
## 141  2020-03-25                   London    113
## 142  2020-03-26                   London    129
## 143  2020-03-27                   London    130
## 144  2020-03-28                   London    122
## 145  2020-03-29                   London    146
## 146  2020-03-30                   London    149
## 147  2020-03-31                   London    181
## 148  2020-04-01                   London    202
## 149  2020-04-02                   London    191
## 150  2020-04-03                   London    196
## 151  2020-04-04                   London    230
## 152  2020-04-05                   London    195
## 153  2020-04-06                   London    197
## 154  2020-04-07                   London    220
## 155  2020-04-08                   London    238
## 156  2020-04-09                   London    206
## 157  2020-04-10                   London    170
## 158  2020-04-11                   London    178
## 159  2020-04-12                   London    158
## 160  2020-04-13                   London    166
## 161  2020-04-14                   London    144
## 162  2020-04-15                   London    142
## 163  2020-04-16                   London    139
## 164  2020-04-17                   London    100
## 165  2020-04-18                   London    101
## 166  2020-04-19                   London    103
## 167  2020-04-20                   London     95
## 168  2020-04-21                   London     94
## 169  2020-04-22                   London    109
## 170  2020-04-23                   London     77
## 171  2020-04-24                   London     71
## 172  2020-04-25                   London     58
## 173  2020-04-26                   London     53
## 174  2020-04-27                   London     51
## 175  2020-04-28                   London     43
## 176  2020-04-29                   London     44
## 177  2020-04-30                   London     40
## 178  2020-05-01                   London     41
## 179  2020-05-02                   London     41
## 180  2020-05-03                   London     36
## 181  2020-05-04                   London     30
## 182  2020-05-05                   London     25
## 183  2020-05-06                   London     37
## 184  2020-05-07                   London     37
## 185  2020-05-08                   London     30
## 186  2020-05-09                   London     23
## 187  2020-05-10                   London     26
## 188  2020-05-11                   London     18
## 189  2020-05-12                   London     18
## 190  2020-05-13                   London     16
## 191  2020-05-14                   London     20
## 192  2020-05-15                   London     18
## 193  2020-05-16                   London     14
## 194  2020-05-17                   London     15
## 195  2020-05-18                   London      9
## 196  2020-05-19                   London     14
## 197  2020-05-20                   London     19
## 198  2020-05-21                   London     12
## 199  2020-05-22                   London     10
## 200  2020-05-23                   London      6
## 201  2020-05-24                   London      7
## 202  2020-05-25                   London      9
## 203  2020-05-26                   London     12
## 204  2020-05-27                   London      7
## 205  2020-05-28                   London      8
## 206  2020-05-29                   London      7
## 207  2020-05-30                   London     12
## 208  2020-05-31                   London      6
## 209  2020-06-01                   London     10
## 210  2020-06-02                   London      7
## 211  2020-06-03                   London      6
## 212  2020-06-04                   London      8
## 213  2020-06-05                   London      4
## 214  2020-06-06                   London      0
## 215  2020-06-07                   London      4
## 216  2020-06-08                   London      5
## 217  2020-06-09                   London      4
## 218  2020-06-10                   London      7
## 219  2020-06-11                   London      5
## 220  2020-06-12                   London      3
## 221  2020-06-13                   London      3
## 222  2020-06-14                   London      2
## 223  2020-06-15                   London      1
## 224  2020-06-16                   London      2
## 225  2020-06-17                   London      1
## 226  2020-06-18                   London      2
## 227  2020-06-19                   London      3
## 228  2020-06-20                   London      3
## 229  2020-06-21                   London      3
## 230  2020-06-22                   London      2
## 231  2020-06-23                   London      0
## 232  2020-06-24                   London      0
## 233  2020-03-01                 Midlands      0
## 234  2020-03-02                 Midlands      0
## 235  2020-03-03                 Midlands      1
## 236  2020-03-04                 Midlands      0
## 237  2020-03-05                 Midlands      0
## 238  2020-03-06                 Midlands      0
## 239  2020-03-07                 Midlands      0
## 240  2020-03-08                 Midlands      3
## 241  2020-03-09                 Midlands      1
## 242  2020-03-10                 Midlands      0
## 243  2020-03-11                 Midlands      2
## 244  2020-03-12                 Midlands      6
## 245  2020-03-13                 Midlands      5
## 246  2020-03-14                 Midlands      4
## 247  2020-03-15                 Midlands      5
## 248  2020-03-16                 Midlands     11
## 249  2020-03-17                 Midlands      8
## 250  2020-03-18                 Midlands     13
## 251  2020-03-19                 Midlands      8
## 252  2020-03-20                 Midlands     28
## 253  2020-03-21                 Midlands     13
## 254  2020-03-22                 Midlands     31
## 255  2020-03-23                 Midlands     33
## 256  2020-03-24                 Midlands     41
## 257  2020-03-25                 Midlands     48
## 258  2020-03-26                 Midlands     64
## 259  2020-03-27                 Midlands     72
## 260  2020-03-28                 Midlands     89
## 261  2020-03-29                 Midlands     92
## 262  2020-03-30                 Midlands     90
## 263  2020-03-31                 Midlands    123
## 264  2020-04-01                 Midlands    140
## 265  2020-04-02                 Midlands    142
## 266  2020-04-03                 Midlands    124
## 267  2020-04-04                 Midlands    151
## 268  2020-04-05                 Midlands    164
## 269  2020-04-06                 Midlands    140
## 270  2020-04-07                 Midlands    123
## 271  2020-04-08                 Midlands    186
## 272  2020-04-09                 Midlands    139
## 273  2020-04-10                 Midlands    127
## 274  2020-04-11                 Midlands    142
## 275  2020-04-12                 Midlands    139
## 276  2020-04-13                 Midlands    120
## 277  2020-04-14                 Midlands    116
## 278  2020-04-15                 Midlands    147
## 279  2020-04-16                 Midlands    102
## 280  2020-04-17                 Midlands    118
## 281  2020-04-18                 Midlands    115
## 282  2020-04-19                 Midlands     92
## 283  2020-04-20                 Midlands    107
## 284  2020-04-21                 Midlands     86
## 285  2020-04-22                 Midlands     78
## 286  2020-04-23                 Midlands    103
## 287  2020-04-24                 Midlands     79
## 288  2020-04-25                 Midlands     72
## 289  2020-04-26                 Midlands     81
## 290  2020-04-27                 Midlands     74
## 291  2020-04-28                 Midlands     68
## 292  2020-04-29                 Midlands     53
## 293  2020-04-30                 Midlands     56
## 294  2020-05-01                 Midlands     64
## 295  2020-05-02                 Midlands     51
## 296  2020-05-03                 Midlands     52
## 297  2020-05-04                 Midlands     61
## 298  2020-05-05                 Midlands     58
## 299  2020-05-06                 Midlands     59
## 300  2020-05-07                 Midlands     48
## 301  2020-05-08                 Midlands     34
## 302  2020-05-09                 Midlands     37
## 303  2020-05-10                 Midlands     42
## 304  2020-05-11                 Midlands     33
## 305  2020-05-12                 Midlands     45
## 306  2020-05-13                 Midlands     40
## 307  2020-05-14                 Midlands     37
## 308  2020-05-15                 Midlands     40
## 309  2020-05-16                 Midlands     34
## 310  2020-05-17                 Midlands     31
## 311  2020-05-18                 Midlands     34
## 312  2020-05-19                 Midlands     34
## 313  2020-05-20                 Midlands     36
## 314  2020-05-21                 Midlands     32
## 315  2020-05-22                 Midlands     27
## 316  2020-05-23                 Midlands     34
## 317  2020-05-24                 Midlands     19
## 318  2020-05-25                 Midlands     26
## 319  2020-05-26                 Midlands     33
## 320  2020-05-27                 Midlands     29
## 321  2020-05-28                 Midlands     27
## 322  2020-05-29                 Midlands     20
## 323  2020-05-30                 Midlands     20
## 324  2020-05-31                 Midlands     22
## 325  2020-06-01                 Midlands     20
## 326  2020-06-02                 Midlands     22
## 327  2020-06-03                 Midlands     24
## 328  2020-06-04                 Midlands     15
## 329  2020-06-05                 Midlands     21
## 330  2020-06-06                 Midlands     20
## 331  2020-06-07                 Midlands     16
## 332  2020-06-08                 Midlands     15
## 333  2020-06-09                 Midlands     17
## 334  2020-06-10                 Midlands     15
## 335  2020-06-11                 Midlands     13
## 336  2020-06-12                 Midlands     12
## 337  2020-06-13                 Midlands      6
## 338  2020-06-14                 Midlands     17
## 339  2020-06-15                 Midlands     12
## 340  2020-06-16                 Midlands     14
## 341  2020-06-17                 Midlands     10
## 342  2020-06-18                 Midlands     14
## 343  2020-06-19                 Midlands      9
## 344  2020-06-20                 Midlands     13
## 345  2020-06-21                 Midlands     12
## 346  2020-06-22                 Midlands     11
## 347  2020-06-23                 Midlands     10
## 348  2020-06-24                 Midlands      0
## 349  2020-03-01 North East and Yorkshire      0
## 350  2020-03-02 North East and Yorkshire      0
## 351  2020-03-03 North East and Yorkshire      0
## 352  2020-03-04 North East and Yorkshire      0
## 353  2020-03-05 North East and Yorkshire      0
## 354  2020-03-06 North East and Yorkshire      0
## 355  2020-03-07 North East and Yorkshire      0
## 356  2020-03-08 North East and Yorkshire      0
## 357  2020-03-09 North East and Yorkshire      0
## 358  2020-03-10 North East and Yorkshire      0
## 359  2020-03-11 North East and Yorkshire      0
## 360  2020-03-12 North East and Yorkshire      0
## 361  2020-03-13 North East and Yorkshire      0
## 362  2020-03-14 North East and Yorkshire      0
## 363  2020-03-15 North East and Yorkshire      2
## 364  2020-03-16 North East and Yorkshire      3
## 365  2020-03-17 North East and Yorkshire      1
## 366  2020-03-18 North East and Yorkshire      2
## 367  2020-03-19 North East and Yorkshire      6
## 368  2020-03-20 North East and Yorkshire      5
## 369  2020-03-21 North East and Yorkshire      6
## 370  2020-03-22 North East and Yorkshire      7
## 371  2020-03-23 North East and Yorkshire      9
## 372  2020-03-24 North East and Yorkshire      8
## 373  2020-03-25 North East and Yorkshire     18
## 374  2020-03-26 North East and Yorkshire     21
## 375  2020-03-27 North East and Yorkshire     28
## 376  2020-03-28 North East and Yorkshire     35
## 377  2020-03-29 North East and Yorkshire     38
## 378  2020-03-30 North East and Yorkshire     64
## 379  2020-03-31 North East and Yorkshire     60
## 380  2020-04-01 North East and Yorkshire     67
## 381  2020-04-02 North East and Yorkshire     74
## 382  2020-04-03 North East and Yorkshire    100
## 383  2020-04-04 North East and Yorkshire    105
## 384  2020-04-05 North East and Yorkshire     92
## 385  2020-04-06 North East and Yorkshire     96
## 386  2020-04-07 North East and Yorkshire    102
## 387  2020-04-08 North East and Yorkshire    107
## 388  2020-04-09 North East and Yorkshire    111
## 389  2020-04-10 North East and Yorkshire    117
## 390  2020-04-11 North East and Yorkshire     98
## 391  2020-04-12 North East and Yorkshire     84
## 392  2020-04-13 North East and Yorkshire     94
## 393  2020-04-14 North East and Yorkshire    107
## 394  2020-04-15 North East and Yorkshire     96
## 395  2020-04-16 North East and Yorkshire    103
## 396  2020-04-17 North East and Yorkshire     88
## 397  2020-04-18 North East and Yorkshire     95
## 398  2020-04-19 North East and Yorkshire     88
## 399  2020-04-20 North East and Yorkshire    100
## 400  2020-04-21 North East and Yorkshire     76
## 401  2020-04-22 North East and Yorkshire     84
## 402  2020-04-23 North East and Yorkshire     63
## 403  2020-04-24 North East and Yorkshire     72
## 404  2020-04-25 North East and Yorkshire     69
## 405  2020-04-26 North East and Yorkshire     65
## 406  2020-04-27 North East and Yorkshire     65
## 407  2020-04-28 North East and Yorkshire     57
## 408  2020-04-29 North East and Yorkshire     69
## 409  2020-04-30 North East and Yorkshire     57
## 410  2020-05-01 North East and Yorkshire     64
## 411  2020-05-02 North East and Yorkshire     48
## 412  2020-05-03 North East and Yorkshire     40
## 413  2020-05-04 North East and Yorkshire     49
## 414  2020-05-05 North East and Yorkshire     40
## 415  2020-05-06 North East and Yorkshire     51
## 416  2020-05-07 North East and Yorkshire     45
## 417  2020-05-08 North East and Yorkshire     42
## 418  2020-05-09 North East and Yorkshire     44
## 419  2020-05-10 North East and Yorkshire     40
## 420  2020-05-11 North East and Yorkshire     29
## 421  2020-05-12 North East and Yorkshire     27
## 422  2020-05-13 North East and Yorkshire     28
## 423  2020-05-14 North East and Yorkshire     31
## 424  2020-05-15 North East and Yorkshire     32
## 425  2020-05-16 North East and Yorkshire     35
## 426  2020-05-17 North East and Yorkshire     26
## 427  2020-05-18 North East and Yorkshire     30
## 428  2020-05-19 North East and Yorkshire     27
## 429  2020-05-20 North East and Yorkshire     22
## 430  2020-05-21 North East and Yorkshire     33
## 431  2020-05-22 North East and Yorkshire     22
## 432  2020-05-23 North East and Yorkshire     18
## 433  2020-05-24 North East and Yorkshire     26
## 434  2020-05-25 North East and Yorkshire     21
## 435  2020-05-26 North East and Yorkshire     21
## 436  2020-05-27 North East and Yorkshire     22
## 437  2020-05-28 North East and Yorkshire     20
## 438  2020-05-29 North East and Yorkshire     25
## 439  2020-05-30 North East and Yorkshire     20
## 440  2020-05-31 North East and Yorkshire     20
## 441  2020-06-01 North East and Yorkshire     16
## 442  2020-06-02 North East and Yorkshire     23
## 443  2020-06-03 North East and Yorkshire     22
## 444  2020-06-04 North East and Yorkshire     17
## 445  2020-06-05 North East and Yorkshire     17
## 446  2020-06-06 North East and Yorkshire     21
## 447  2020-06-07 North East and Yorkshire     14
## 448  2020-06-08 North East and Yorkshire     11
## 449  2020-06-09 North East and Yorkshire     11
## 450  2020-06-10 North East and Yorkshire     18
## 451  2020-06-11 North East and Yorkshire      7
## 452  2020-06-12 North East and Yorkshire      9
## 453  2020-06-13 North East and Yorkshire     10
## 454  2020-06-14 North East and Yorkshire     11
## 455  2020-06-15 North East and Yorkshire      8
## 456  2020-06-16 North East and Yorkshire     10
## 457  2020-06-17 North East and Yorkshire      8
## 458  2020-06-18 North East and Yorkshire     10
## 459  2020-06-19 North East and Yorkshire      6
## 460  2020-06-20 North East and Yorkshire      4
## 461  2020-06-21 North East and Yorkshire      4
## 462  2020-06-22 North East and Yorkshire      6
## 463  2020-06-23 North East and Yorkshire      5
## 464  2020-06-24 North East and Yorkshire      1
## 465  2020-03-01               North West      0
## 466  2020-03-02               North West      0
## 467  2020-03-03               North West      0
## 468  2020-03-04               North West      0
## 469  2020-03-05               North West      1
## 470  2020-03-06               North West      0
## 471  2020-03-07               North West      0
## 472  2020-03-08               North West      1
## 473  2020-03-09               North West      0
## 474  2020-03-10               North West      0
## 475  2020-03-11               North West      0
## 476  2020-03-12               North West      2
## 477  2020-03-13               North West      3
## 478  2020-03-14               North West      1
## 479  2020-03-15               North West      4
## 480  2020-03-16               North West      2
## 481  2020-03-17               North West      4
## 482  2020-03-18               North West      6
## 483  2020-03-19               North West      7
## 484  2020-03-20               North West     10
## 485  2020-03-21               North West     11
## 486  2020-03-22               North West     13
## 487  2020-03-23               North West     15
## 488  2020-03-24               North West     21
## 489  2020-03-25               North West     21
## 490  2020-03-26               North West     29
## 491  2020-03-27               North West     35
## 492  2020-03-28               North West     28
## 493  2020-03-29               North West     46
## 494  2020-03-30               North West     67
## 495  2020-03-31               North West     52
## 496  2020-04-01               North West     86
## 497  2020-04-02               North West     96
## 498  2020-04-03               North West     95
## 499  2020-04-04               North West     98
## 500  2020-04-05               North West    102
## 501  2020-04-06               North West    100
## 502  2020-04-07               North West    135
## 503  2020-04-08               North West    127
## 504  2020-04-09               North West    119
## 505  2020-04-10               North West    117
## 506  2020-04-11               North West    138
## 507  2020-04-12               North West    125
## 508  2020-04-13               North West    129
## 509  2020-04-14               North West    131
## 510  2020-04-15               North West    114
## 511  2020-04-16               North West    135
## 512  2020-04-17               North West     98
## 513  2020-04-18               North West    113
## 514  2020-04-19               North West     71
## 515  2020-04-20               North West     83
## 516  2020-04-21               North West     76
## 517  2020-04-22               North West     86
## 518  2020-04-23               North West     85
## 519  2020-04-24               North West     66
## 520  2020-04-25               North West     65
## 521  2020-04-26               North West     55
## 522  2020-04-27               North West     54
## 523  2020-04-28               North West     57
## 524  2020-04-29               North West     62
## 525  2020-04-30               North West     59
## 526  2020-05-01               North West     45
## 527  2020-05-02               North West     56
## 528  2020-05-03               North West     55
## 529  2020-05-04               North West     48
## 530  2020-05-05               North West     48
## 531  2020-05-06               North West     44
## 532  2020-05-07               North West     49
## 533  2020-05-08               North West     42
## 534  2020-05-09               North West     30
## 535  2020-05-10               North West     41
## 536  2020-05-11               North West     35
## 537  2020-05-12               North West     38
## 538  2020-05-13               North West     25
## 539  2020-05-14               North West     26
## 540  2020-05-15               North West     33
## 541  2020-05-16               North West     32
## 542  2020-05-17               North West     24
## 543  2020-05-18               North West     31
## 544  2020-05-19               North West     35
## 545  2020-05-20               North West     27
## 546  2020-05-21               North West     26
## 547  2020-05-22               North West     26
## 548  2020-05-23               North West     31
## 549  2020-05-24               North West     26
## 550  2020-05-25               North West     31
## 551  2020-05-26               North West     27
## 552  2020-05-27               North West     27
## 553  2020-05-28               North West     28
## 554  2020-05-29               North West     20
## 555  2020-05-30               North West     19
## 556  2020-05-31               North West     13
## 557  2020-06-01               North West     12
## 558  2020-06-02               North West     27
## 559  2020-06-03               North West     22
## 560  2020-06-04               North West     22
## 561  2020-06-05               North West     15
## 562  2020-06-06               North West     23
## 563  2020-06-07               North West     19
## 564  2020-06-08               North West     20
## 565  2020-06-09               North West     15
## 566  2020-06-10               North West     14
## 567  2020-06-11               North West     16
## 568  2020-06-12               North West      8
## 569  2020-06-13               North West      8
## 570  2020-06-14               North West     15
## 571  2020-06-15               North West     15
## 572  2020-06-16               North West     11
## 573  2020-06-17               North West     10
## 574  2020-06-18               North West     11
## 575  2020-06-19               North West      7
## 576  2020-06-20               North West     11
## 577  2020-06-21               North West      6
## 578  2020-06-22               North West     10
## 579  2020-06-23               North West      8
## 580  2020-06-24               North West      4
## 581  2020-03-01               South East      0
## 582  2020-03-02               South East      0
## 583  2020-03-03               South East      1
## 584  2020-03-04               South East      0
## 585  2020-03-05               South East      1
## 586  2020-03-06               South East      0
## 587  2020-03-07               South East      0
## 588  2020-03-08               South East      1
## 589  2020-03-09               South East      1
## 590  2020-03-10               South East      1
## 591  2020-03-11               South East      1
## 592  2020-03-12               South East      0
## 593  2020-03-13               South East      1
## 594  2020-03-14               South East      1
## 595  2020-03-15               South East      5
## 596  2020-03-16               South East      8
## 597  2020-03-17               South East      7
## 598  2020-03-18               South East     10
## 599  2020-03-19               South East      9
## 600  2020-03-20               South East     13
## 601  2020-03-21               South East      7
## 602  2020-03-22               South East     25
## 603  2020-03-23               South East     20
## 604  2020-03-24               South East     22
## 605  2020-03-25               South East     29
## 606  2020-03-26               South East     35
## 607  2020-03-27               South East     34
## 608  2020-03-28               South East     36
## 609  2020-03-29               South East     55
## 610  2020-03-30               South East     58
## 611  2020-03-31               South East     65
## 612  2020-04-01               South East     66
## 613  2020-04-02               South East     55
## 614  2020-04-03               South East     72
## 615  2020-04-04               South East     80
## 616  2020-04-05               South East     82
## 617  2020-04-06               South East     88
## 618  2020-04-07               South East    100
## 619  2020-04-08               South East     83
## 620  2020-04-09               South East    104
## 621  2020-04-10               South East     88
## 622  2020-04-11               South East     88
## 623  2020-04-12               South East     88
## 624  2020-04-13               South East     84
## 625  2020-04-14               South East     65
## 626  2020-04-15               South East     72
## 627  2020-04-16               South East     56
## 628  2020-04-17               South East     86
## 629  2020-04-18               South East     57
## 630  2020-04-19               South East     70
## 631  2020-04-20               South East     87
## 632  2020-04-21               South East     50
## 633  2020-04-22               South East     54
## 634  2020-04-23               South East     57
## 635  2020-04-24               South East     64
## 636  2020-04-25               South East     51
## 637  2020-04-26               South East     51
## 638  2020-04-27               South East     40
## 639  2020-04-28               South East     40
## 640  2020-04-29               South East     47
## 641  2020-04-30               South East     29
## 642  2020-05-01               South East     37
## 643  2020-05-02               South East     36
## 644  2020-05-03               South East     17
## 645  2020-05-04               South East     35
## 646  2020-05-05               South East     29
## 647  2020-05-06               South East     25
## 648  2020-05-07               South East     27
## 649  2020-05-08               South East     26
## 650  2020-05-09               South East     28
## 651  2020-05-10               South East     19
## 652  2020-05-11               South East     25
## 653  2020-05-12               South East     27
## 654  2020-05-13               South East     18
## 655  2020-05-14               South East     32
## 656  2020-05-15               South East     24
## 657  2020-05-16               South East     22
## 658  2020-05-17               South East     18
## 659  2020-05-18               South East     22
## 660  2020-05-19               South East     12
## 661  2020-05-20               South East     22
## 662  2020-05-21               South East     15
## 663  2020-05-22               South East     17
## 664  2020-05-23               South East     21
## 665  2020-05-24               South East     17
## 666  2020-05-25               South East     13
## 667  2020-05-26               South East     19
## 668  2020-05-27               South East     18
## 669  2020-05-28               South East     12
## 670  2020-05-29               South East     21
## 671  2020-05-30               South East      8
## 672  2020-05-31               South East     10
## 673  2020-06-01               South East     11
## 674  2020-06-02               South East     13
## 675  2020-06-03               South East     17
## 676  2020-06-04               South East     11
## 677  2020-06-05               South East     11
## 678  2020-06-06               South East     10
## 679  2020-06-07               South East     11
## 680  2020-06-08               South East      7
## 681  2020-06-09               South East     10
## 682  2020-06-10               South East     10
## 683  2020-06-11               South East      5
## 684  2020-06-12               South East      5
## 685  2020-06-13               South East      4
## 686  2020-06-14               South East      6
## 687  2020-06-15               South East      7
## 688  2020-06-16               South East     10
## 689  2020-06-17               South East      8
## 690  2020-06-18               South East      4
## 691  2020-06-19               South East      6
## 692  2020-06-20               South East      4
## 693  2020-06-21               South East      3
## 694  2020-06-22               South East      2
## 695  2020-06-23               South East      2
## 696  2020-06-24               South East      0
## 697  2020-03-01               South West      0
## 698  2020-03-02               South West      0
## 699  2020-03-03               South West      0
## 700  2020-03-04               South West      0
## 701  2020-03-05               South West      0
## 702  2020-03-06               South West      0
## 703  2020-03-07               South West      0
## 704  2020-03-08               South West      0
## 705  2020-03-09               South West      0
## 706  2020-03-10               South West      0
## 707  2020-03-11               South West      1
## 708  2020-03-12               South West      0
## 709  2020-03-13               South West      0
## 710  2020-03-14               South West      1
## 711  2020-03-15               South West      0
## 712  2020-03-16               South West      0
## 713  2020-03-17               South West      2
## 714  2020-03-18               South West      2
## 715  2020-03-19               South West      4
## 716  2020-03-20               South West      3
## 717  2020-03-21               South West      6
## 718  2020-03-22               South West      7
## 719  2020-03-23               South West      8
## 720  2020-03-24               South West      7
## 721  2020-03-25               South West      9
## 722  2020-03-26               South West     11
## 723  2020-03-27               South West     13
## 724  2020-03-28               South West     21
## 725  2020-03-29               South West     18
## 726  2020-03-30               South West     23
## 727  2020-03-31               South West     23
## 728  2020-04-01               South West     22
## 729  2020-04-02               South West     23
## 730  2020-04-03               South West     30
## 731  2020-04-04               South West     42
## 732  2020-04-05               South West     32
## 733  2020-04-06               South West     34
## 734  2020-04-07               South West     39
## 735  2020-04-08               South West     47
## 736  2020-04-09               South West     24
## 737  2020-04-10               South West     46
## 738  2020-04-11               South West     43
## 739  2020-04-12               South West     23
## 740  2020-04-13               South West     27
## 741  2020-04-14               South West     24
## 742  2020-04-15               South West     32
## 743  2020-04-16               South West     29
## 744  2020-04-17               South West     33
## 745  2020-04-18               South West     25
## 746  2020-04-19               South West     31
## 747  2020-04-20               South West     26
## 748  2020-04-21               South West     26
## 749  2020-04-22               South West     23
## 750  2020-04-23               South West     17
## 751  2020-04-24               South West     19
## 752  2020-04-25               South West     15
## 753  2020-04-26               South West     27
## 754  2020-04-27               South West     13
## 755  2020-04-28               South West     17
## 756  2020-04-29               South West     15
## 757  2020-04-30               South West     26
## 758  2020-05-01               South West      6
## 759  2020-05-02               South West      7
## 760  2020-05-03               South West     10
## 761  2020-05-04               South West     17
## 762  2020-05-05               South West     14
## 763  2020-05-06               South West     19
## 764  2020-05-07               South West     16
## 765  2020-05-08               South West      6
## 766  2020-05-09               South West     11
## 767  2020-05-10               South West      5
## 768  2020-05-11               South West      8
## 769  2020-05-12               South West      7
## 770  2020-05-13               South West      7
## 771  2020-05-14               South West      6
## 772  2020-05-15               South West      4
## 773  2020-05-16               South West      4
## 774  2020-05-17               South West      6
## 775  2020-05-18               South West      4
## 776  2020-05-19               South West      6
## 777  2020-05-20               South West      1
## 778  2020-05-21               South West      9
## 779  2020-05-22               South West      6
## 780  2020-05-23               South West      6
## 781  2020-05-24               South West      3
## 782  2020-05-25               South West      8
## 783  2020-05-26               South West     11
## 784  2020-05-27               South West      5
## 785  2020-05-28               South West     10
## 786  2020-05-29               South West      7
## 787  2020-05-30               South West      3
## 788  2020-05-31               South West      2
## 789  2020-06-01               South West      7
## 790  2020-06-02               South West      2
## 791  2020-06-03               South West      5
## 792  2020-06-04               South West      2
## 793  2020-06-05               South West      2
## 794  2020-06-06               South West      1
## 795  2020-06-07               South West      3
## 796  2020-06-08               South West      3
## 797  2020-06-09               South West      0
## 798  2020-06-10               South West      0
## 799  2020-06-11               South West      2
## 800  2020-06-12               South West      2
## 801  2020-06-13               South West      2
## 802  2020-06-14               South West      0
## 803  2020-06-15               South West      1
## 804  2020-06-16               South West      1
## 805  2020-06-17               South West      0
## 806  2020-06-18               South West      0
## 807  2020-06-19               South West      0
## 808  2020-06-20               South West      2
## 809  2020-06-21               South West      0
## 810  2020-06-22               South West      1
## 811  2020-06-23               South West      0
## 812  2020-06-24               South West      0

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-06-25"

The completion date of the NHS Pathways data is Thursday 25 Jun 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -10.1993   -2.5629   -0.3803    3.4485    5.6660  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.875e+00  5.375e-02   90.70   <2e-16 ***
## note_lag    1.223e-05  5.454e-07   22.42   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 12.90006)
## 
##     Null deviance: 6906.98  on 54  degrees of freedom
## Residual deviance:  704.64  on 53  degrees of freedom
##   (23 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 4

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##  130.942881    1.000012
exp(confint(lag_mod))
##                  2.5 %     97.5 %
## (Intercept) 117.705519 145.313867
## note_lag      1.000011   1.000013

Rsq(lag_mod)
## [1] 0.8979809

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                            sysname 
##                                                                                           "Darwin" 
##                                                                                            release 
##                                                                                           "19.5.0" 
##                                                                                            version 
## "Darwin Kernel Version 19.5.0: Tue May 26 20:41:44 PDT 2020; root:xnu-6153.121.2~2/RELEASE_X86_64" 
##                                                                                           nodename 
##                                                                                   "Mac-1540.local" 
##                                                                                            machine 
##                                                                                           "x86_64" 
##                                                                                              login 
##                                                                                             "root" 
##                                                                                               user 
##                                                                                           "runner" 
##                                                                                     effective_user 
##                                                                                           "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin15.6.0   
## arch           x86_64                      
## os             darwin15.6.0                
## system         x86_64, darwin15.6.0        
## status                                     
## major          3                           
## minor          6.3                         
## year           2020                        
## month          02                          
## day            29                          
## svn rev        77875                       
## language       R                           
## version.string R version 3.6.3 (2020-02-29)
## nickname       Holding the Windsock

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 3.6.3 (2020-02-29)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS Catalina 10.15.5
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.1     ggpubr_0.3.0         lubridate_1.7.9     
##  [4] chngpt_2020.5-21     cyphr_1.1.0          DT_0.14             
##  [7] kableExtra_1.1.0     janitor_2.0.1        remotes_2.1.1       
## [10] projections_0.5.0    earlyR_0.0.1         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.1      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.5          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.0          purrr_0.3.4          readr_1.3.1         
## [25] tidyr_1.1.0          tibble_3.0.1         ggplot2_3.3.2       
## [28] tidyverse_1.3.0      here_0.1             reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] colorspace_1.4-1  selectr_0.4-2     ggsignif_0.6.0    ellipsis_0.3.1   
##  [5] rprojroot_1.3-2   snakecase_0.11.0  fs_1.4.1          rstudioapi_0.11  
##  [9] farver_2.0.3      fansi_0.4.1       splines_3.6.3     knitr_1.29       
## [13] jsonlite_1.7.0    broom_0.5.6       dbplyr_1.4.4      compiler_3.6.3   
## [17] httr_1.4.1        backports_1.1.8   assertthat_0.2.1  Matrix_1.2-18    
## [21] cli_2.0.2         htmltools_0.5.0   prettyunits_1.1.1 tools_3.6.3      
## [25] gtable_0.3.0      glue_1.4.1        Rcpp_1.0.4.6      carData_3.0-4    
## [29] cellranger_1.1.0  vctrs_0.3.1       nlme_3.1-144      matchmaker_0.1.1 
## [33] crosstalk_1.1.0.1 xfun_0.15         ps_1.3.3          openxlsx_4.1.5   
## [37] lifecycle_0.2.0   rstatix_0.6.0     MASS_7.3-51.5     scales_1.1.1     
## [41] hms_0.5.3         sodium_1.1        yaml_2.2.1        curl_4.3         
## [45] gridExtra_2.3     stringi_1.4.6     kyotil_2019.11-22 boot_1.3-24      
## [49] pkgbuild_1.0.8    zip_2.0.4         rlang_0.4.6       pkgconfig_2.0.3  
## [53] evaluate_0.14     lattice_0.20-38   labeling_0.3      htmlwidgets_1.5.1
## [57] cowplot_1.0.0     processx_3.4.2    tidyselect_1.1.0  plyr_1.8.6       
## [61] magrittr_1.5      R6_2.4.1          generics_0.0.2    DBI_1.1.0        
## [65] pillar_1.4.4      haven_2.3.1       foreign_0.8-75    withr_2.2.0      
## [69] mgcv_1.8-31       survival_3.1-8    abind_1.4-5       modelr_0.1.8     
## [73] crayon_1.3.4      car_3.0-8         utf8_1.1.4        rmarkdown_2.3    
## [77] viridis_0.5.1     grid_3.6.3        readxl_1.3.1      data.table_1.12.8
## [81] blob_1.2.1        callr_3.4.3       reprex_0.3.0      digest_0.6.25    
## [85] webshot_0.5.2     munsell_0.5.0     viridisLite_0.3.0